Apopulation of 100 frogs increases at an annual rate of 22% how many frogs will there be in 10 years

Because the number of frogs is increasing by the same ratio each year, this problem can be solved by the equation for a geometric progression. That equation is shown below:

xn = arn-1

where xn = the value of x after n terms
a = the initial value
r = the ratio of each term to the one before it (e.g. x2/x1)

For this case, we are starting with an initial value (a) of 100. After that there will be 5 more terms in the progression representing the value after each of the 5 years. So there are a total of 6 terms in the progression meaning that n= 6.

The ratio (r) which is the amount being multiplied each year is 1.22 because the rate is increasing by 22% each year.

Plugging these values for a, n, and r into the equation above gives:

xn = (100)(1.22)5
xn = (100)(2.7027)
xn = 270.3

Therefore, the value after 5 years is $270.27